Following are digitized figures for stress concentration factors

They are taken from pp. 82-85 of the text.

Centered hole in tension

For a centered hole under tension, $K_{tg}$ uses stress for the cross-sectional area if no hole was present, $K_{tn}$ uses stress at the net section (subtracting hole area). $a$ is the hole diameter, $W$ is specimen width.

In [2]:
#this code is just to load the necessary libraries
import plotly.graph_objects as go

#load saved data
import pickle

#load saved plot.ly figures
with open('../plotlyfigs/stress-concentration.pickle','rb') as f:
    fig=pickle.load(f)
In [3]:
#plot first figure
test = go.Figure(fig[0])
test.show(config={"showLink": True},renderer="notebook")

Off-center hole in tension

For an off-center hole under tension, we have $K_{tg}$ uses stress for the cross-sectional area if no hole was present, $K_{tn}$ uses stress at the net section (subtracting hole area). $c$ is the distance from the closest edge to the center of the hole, $e$ is the distance from the farthest edge to the center of the hole, $r$ is hole radius.

In [4]:
test = go.Figure(fig[1])
test.show(config={"showLink": True},renderer="notebook")

Bending of a bar with U-shaped notch

For the bending of a bar with a U-shaped notch, we have the following parameters: Nominal stress used for $K_t$ is given by $\sigma_{nom} = 6M/hd^2$ where $M$ is applied bending moment, $h$ is thickness, $d$ is the net-section height (height minus notch depth). $D$ is the height of the panel without a notch and $r$ is the notch radius.

In [5]:
test = go.Figure(fig[2])
test.show(config={"showLink": True},renderer="notebook")

Tension of a stepped bar with should fillets

For the tension of a stepped bar with shoulder fillets, we have the paraemters: $D$ is the larger width (before the step), $d$ is the width after the step. Nominal stress is $\sigma_{nom} = P/hd$, where $h$ is specimen thickness. $r$ is the fillet radius.

In [6]:
test = go.Figure(fig[3])
test.show(config={"showLink": True},renderer="notebook")
In [ ]: